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Conflicts between intuitive and analytic results 51
while the aggregate value of benefits for Q will be:
(40 × 100) + (60 × 0) = 4000, i.e. 40 after dividing by 100
This clearly suggests that the decision maker should choose office P.
However, it may be that he considers image only to be of value if the office
is highly visible. Office P’s good image is, he thinks, virtually worthless
because it is not on a highly visible location and he might therefore
prefer office Q. Thus, if image is not preference independent of visibility,
the additive model will not correctly represent the owner’s preferences.
How can the absence of mutual preference independence be identified?
The most obvious way in which this will reveal itself is in the use of
phrases like ‘this depends on ...’ when the decision maker responds to
questions. For example, when asked to assign a value to the ‘image’ of
an office, our decision maker might well have said ‘that depends on how
visible the office is’.
If mutual preference independence does not exist it is usually possible
to return to the value tree and redefine the attributes so that a set of
attributes which are mutually preference independent can be identified.
For example, perhaps visibility and image could be replaced by a single
attribute ‘ability to attract casual customers’.
In the occasional problems where this is not possible, other models
are available which can handle the interaction between the attributes.
The most well known of these is the multiplicative model. Consider
again the case of the house purchase decision where the quality of the
architecture and attractiveness of the garden complemented each other.
If we let V(A) = the value of the architecture of a given house and
V(G) = a value for the attractiveness of the garden then we might find
that the following represented the overall value of the house:
Value = 0.6V(A) + 0.3V(G) + 0.1V(A)V(G)
The numbers in the above expression represent the weights (note that
they sum to 1) and the last expression, which involves multiplying
the values together, represents the interaction between architecture and
garden. Because the multiplicative model is not widely used we will not
consider it in detail. Longer discussions can be found in Bodily 12 and
von Winterfeldt and Edwards. 10
Conflicts between intuitive and analytic results
It may be that, if the decision maker had viewed the problem holistically,
then he would have ranked his preferences for the offices in a very